Thanks for your great input, @OC Richard! Indeed, my first attempts were way more true to the coat of arms, leading to designs that were either unappealing or did not look anything like tartans. To get a good "tartan feel" to it, I skimmed through dozens and dozens of designs, until I realized that I really like the construction of Québec's. Hence I used this pattern with the colors of the coat of arms, added the three stripes and some other minor tweaks, leading to my proposal above. Now certainly it does not respect the order given by the blazon, but I feel it is still somewhat faithful, and—also importantly—appealing. That the structure is given by Québec's tartan is thus but a lucky coincidence :-)

Cheers!